Barbieri et al.: Yield-per-recruit analysis for Micropogonias undulatus 
639 
Table 1 
Parameter estimates or range of values used in yield-per- 
recruit simulations for Atlantic croaker, Micropogonias 
undulatus, in the lower Chesapeake Bay (period 1988-91) 
and North Carolina (period 1979-81). See Equation 1 for 
definitions of parameter variables. 
Parameter 
Chesapeake Bay 
North Carolina 
K 
0.36 
0.20 
409.9 g 
3,814 g 
*0 
-3.26 yr 
-0.60 yr 
t r 
0 yr 
0 yr 
tc 
1-5 yr 
1-5 yr 
F 
0.01-2.0 
0.01-2.0 
M 
0.20-0.35 
0.20-0.35 
Bay (Barbieri et al., 1994a). To estimate current lev- 
els of fishing mortality (F CUR ) for different values of 
M, we used Z = 0.60 for Chesapeake Bay and Z = 1.3 
for North Carolina, as 
F cur = Z - Mi , ( 2 ) 
where i - 0.20, 0.25, 0.30, and 0.35. 
The value of F 0 x (the level of F for which the mar- 
ginal increase in yield-per-recruit due to a small in- 
crease in F is 10% of the marginal yield-per-recruit 
in a lightly-exploited fishery [Gulland and Boerema, 
1973; Anthony 2 ]), was estimated for Chesapeake Bay 
with F = 0.01 and t c = 2 (Barbieri et al., 1994a) and for 
North Carolina with F = 0.01 and t c = 1 (Ross, 1988). 
Cohort biomass and harvesting time 
In general, the maximum possible yield for a given 
year class occurs at the critical age t CRITIC , the age 
where biomass of a cohort is maximum in the ab- 
sence of fishing. For comparison with the Beverton- 
Holt yield-per-recruit modeling results, we estimated 
t critic f° r Atlantic croaker following Alverson and 
Carney (1975) and Deriso (1987) as 
t CRITlC =t 0 + — ln(3if/M+ 1), (3) 
where t 0 , K, and M are defined as in Equation 1. 
Parameter estimates or the range of values used in 
calculations are listed in Table 1. 
2 Anthony, V. 1982. The calculation of F 0 p a plea for standard- 
ization. Northwest Atlantic Fisheries Organization, SCR Doc. 
82/VI/64 Ser. No. N557, 15 p. NAFO, PO Box 638, Dartmouth, 
Nova Scotia, Canada B2Y 3Y9. 
To evaluate the proportion of the potential growth 
span (P ) remaining when Atlantic croaker enter the 
exploited phase of life (Beverton and Holt, 1957), we 
used the quantity (Beverton, 1963): 
P g = (l-l c /LJ, (4) 
where L m , the asymptotic length, was obtained from 
Barbieri et al. (1994a) and Ross (1988) and l c , the 
average length at first capture, was obtained by con- 
verting t to length with the von Bertalanffy growth 
curve reported for Atlantic croaker in Chesapeake Bay 
(Barbieri et al., 1994a) and North Carolina (Ross, 1988). 
Both parameters are based on total length (TL) in mm. 
Results 
Chesapeake Bay 
Curves of yield-per-recruit on F (Fig. 1) showed that 
the yield of Atlantic croaker in Chesapeake Bay could 
be maximized by decreasing the current level of t c = 2 
(265 mm TL) to t c = 1 (245 mm TL). Independent of 
the level of M or F used in simulations, yield-per- 
recruit values were consistently higher at t = 1 and 
decreased continuously with increasing t c . However, 
increases in yield from t = 2 to t = 1 were generally 
small and gradually increased with increases in M. 
For example, at the estimated current levels of fish- 
ing mortality for Atlantic croaker in the Chesapeake 
Bay (F cur ), increases in yield between t c = 2 and t c = 1 
would be 7.1% at M = 2.0, 12.6% at M = 0.25, 18.4% 
at M = 0.30, and 24.6% at AT = 0.35. 
The curves of yield-per-recruit for Atlantic croaker 
on F for different levels of M and t c showed no clearly 
defined peaks. Although the magnitude of yield 
curves was dependent on the level of M used in simu- 
lations, relative changes in yield as a function of F 
and t c were very similar, regardless of M (Fig. 1). For 
all levels of M and t , yield curves increased rapidly 
in the range of F between 0 and 0.50-0.75, and re- 
mained relatively flat thereafter. Although yield val- 
ues increased continuously with F, i.e. maximum 
yield-per-recruit always occurred at the maximum 
value of F used in simulations (F=2.0), increases in 
yield beyond F = 0.50-0.75 were very small. For ex- 
ample, increases in yield from F = 0.75 to F MAX ranged 
from 5.3% to 22.7%, depending on the level of M and 
t used in the model (Table 2). However, this rela- 
tively small gain in yield corresponds to an increase 
in F of 166.7%. 
For the range of M used in our study, estimates of 
F CUR are below the levels that give maximum poten- 
tial yield-per-recruit ( F MAX ) and, for M > 0.3, below 
